A new way of gambling is not really patentable subject matter, as it is almost certainly an abstract idea. Abstract ideas are excluded from patentability in the US. Although there is no single definition of abstract idea, the 2014 Interim Guidance on Subject Matter Eligibility provides:
Abstract ideas have been identified by the courts by way of example, including fundamental economic practices, certain methods of organizing human activities, an idea 'of itself, and mathematical relationships/formulas.
What can you do?
You would need to further develop your gambling method to be more than abstract. It is hard to be precise in this. However, a new, unique device that enables the betting method might be patentable (even if the method itself is not).